F factor method for determining heat rate and emission rates of a fossil-fired system

ABSTRACT

The operation of a fossil-fueled thermal system is quantified by employing the F Factor and other operating parameters to determine and monitor the unit&#39;s heat rate and to determine the emission rates of its pollutants.

This application is a Continuation-In-Part of U.S. patent application Ser. No. 09/59,061 filed Jan. 11, 2001, for which priority is claimed and whose disclosure is hereby incorporated by reference; application Ser. No. 9/759,061 is in turn a Continuation-In-Part of U.S. patent application Ser. No. 09/273,711 filed Mar. 22, 1999 now U.S. Pat. No. 6,522,994, for which priority is claimed and whose disclosure is hereby incorporated by reference in its entirety; application Ser. No. 09/273,711 is in turn s Continuation-In-Part of U.S. patent application Ser. No. 09/047,198 filed Mar. 24, 1998 now abandoned, for which priority is claimed and whose disclosure is hereby incorporated by reference in its entirety.

This invention relates to a fossil-fired power plant or steam generation thermal system, and, more particularly, to a method for determining its heat rate from the total effluents flow, the EPA's F Factor and other operating parameters. It further teaches how the F Factor may be used to determine the system's emission rates of pollutants from fossil combustion.

BACKGROUND OF THE INVENTION

The importance of determining a fossil-fired power plant's or steam generation system's heat rate (inversely related to thermal efficiency) is critical if practical day-to-day improvements in heat rate are to be made, and/or problems in thermally degraded equipment are to be found and corrected. Although elaborate analytical tools are sometimes needed, simpler and less expensive methods are also applicable which do not require high maintenance nor the input of complex operational system data, and, also, whose accuracy is not greatly compromised. Both the F Factor and the L Factor methods address this need.

General background of this invention is discussed at length in spplication Ser. No. 09/273,711 (hereinafter denoted as '711), and in application Ser. No. 09/047,198 (hereinafter denoted as '198). In '711 the L Factor is termed the “fuel factor”.

As discussed in '711, related artto the present invention was developed by Roughton in 1980; see J. E. Roughton, “A Proposed On-Line Efficiency Method for Pulverized-Coal-Fired Boilers”, Journal ofthe Institute of Energy, Vol.20, March 1980, pages 20-24. His approach using the L Factor (termed M_(d)/I_(d) in his work) in developing boiler efficiency was to compute system losses such that η_(Boiler)=1.0−Σ (System Losses). This is a version of the Heat Loss Method discussed in '711. The principle losses he considered were associated with dry total effluents (termed stack losses), effluent moisture loss and unburned carbon loss. Roughton's method produces boiler efficiency independent of any measured fuel flow and independent of any measured total effluents flow.

Related art known to the inventor since '711 and '198 were filed is the technical paper: S. S. Munukutla, “Heat Rate Monitoring Options for Coal-Fired Power Plants”, Proceedings of Heat Rate Improvement Conference, Baltimore, Md., sponsored by Electric Power Research Institute, September 1998. In this paper Munukutla explains 40 CFR Part 60, Appendix A, Method 19, and the use of its F Factor to determine heat rate. Munukutla makes no mention of correction factors, neither conceptual nor those associated with measurement error. He concludes “. . . that the heat rate, as determined bythe F-factor method, is in error by at least 10-20%.” In his “Conclusions” section, Munukutla states that: “The F Factor method may give accurate results, provided the stack gas flow rate and CO₂ concentration can be measured accurately.” He makes no mention of the molecular weight, or assumed composition, of the total effluents from combustion. Further, Munukutla explicitly states in his writing and by equation that system heat rate is inversely proportional to the concentration of effluent CO₂.

Other related art is the technical presentation by N. Sarunac, C. E. Romero and E. K. Levy entitled “F-Factor Method for Heat Rate Measurement and its Characteristics”, presented at the Electric Power Research Institute's (EPRI) Twelfth Heat Rate Improvement Conference, Jan. 30 to Feb. 1, 2001, Dallas, Tex. and available from the proceedings (EPRI, Palo Alto, Calif.). This work discusses the CO₂ based F_(C) Factor and the O₂ based F_(D) Factor and their use in determining system heat rate. They stated that the F Factor method is not used due to its low precision and accuracy, siting 5 to 25% error compared to conventional heat rate methods. The authors site the principal sources of error as being the flue gas flow rate, and either the CO₂ concentration or the O₂ concentration measurement in the effluent. They discuss methods of improving the measurement accuracy of these quantities. These authors also indicate by equation that heat rate is inversely proportional to the concentration of effluent CO₂ or O₂.

Related art to the present invention also includes the EPA's F Factor method, discussed in '711, and whose procedures are specified in Chapter 40 of the Code of Federal Regulations (40 CFR), Part 60, Appendix A, Method 19. Assumed by Method 19 is that an F_(C), F_(D) or F_(W) Factor is the ratio of a gas volume (of CO₂ or O₂) found in the combustion products to the heat content of the fuel.

SUMMARY OF THE INVENTION

The monitoring ofafossil-fired system may involve detailed and complete descriptive understanding of the fuel being burned, analyses of all major components, and accurate determination of its fuel flow. Such monitoring is possible by applying the Input/Loss Method discussed in '711 and '198. However, for many fossil-fired systems simpler methods are needed which allow the installation of analytical tools which provide an inexpensive, but consistent, indication of a system's thermal performance. From such indication, the system's efficiency may be monitored, deviations found, and corrections implemented. This invention discloses such atool. Its accuracy is not at the level of the Input/Loss Method, but has been found to be within 1% to 2% when monitoring on-line, and, as importantly, has been demonstrated to be consistent.

This invention employs both the L Factor and F Factor to determine system heat rate. Although the heat rate computed using the EPA's F Factor may not be as accurate as one determined from the L Factor, its accuracy still may be tolerable and useful given the ease in its computation. The L Factor and the F Factor may be used to determine heat rate only if certain correction factors are applied as taught by this invention. These correction factors are both conceptual and for routine measurement error.

The present invention, termed the F Factor Method, determines total fuel energy flow of a fossil-fired system resulting, when the total fuel energy flow is divided by the measured system electrical output, the heat rate of the system. Acceptable heat rate accuracy is achievable through the demonstrated high consistency found in a corrected L Factor based on the F Factor, to which this invention makes unique advantage.

The F Factor method does not use any part of the Heat Loss Method, it does not compute nor need any thermal loss term as used by Roughton. Unlike Roughton's method, the F Factor method employs the principle effluent flow or fuel flow associated with afossil-fired system.

This invention is unlike the works of Munukutla and Sarunac, et al, several key areas. First, as taught by this invention, system heat rate using the F Factor is directly proportional to the concentration of effluent CO₂, not inversely proportional as stated by these authors. Further, this effluent CO₂ is associated with theoretical combustion, not actual combustion as these authors believe; but the actual value may be corrected to the theoretical. Further, it has occurred during the development of this invention that certain conceptual correction factors must be applied to the F Factor to correctly and accurately monitor a fossil-fired system. No corrections of any kind are mentioned by these authors. This is significant to this invention for the F Factor affords one method of computing the L Factor, however conceptual corrections which have been found to apply to the L Factor, also fundamentally apply to the F Factor. And lastly, these authors make no mention ofthe molecular weight, or alternatively the assumed composition, or alternatively the density of the total effluents being produced which this invention teaches must be addressed as different fossil fuels produce different mixes of combustion products comprising the total effluents.

In the process leading to the present invention, several problems existing with the F Factor concept have been both clarified and solutions found. These problems include the following: 1) large conventionally fired power plants have air in-leakage which alters the total effluents concentration's average molecular weight from base assumptions; 2) different Ranks of coal will produce different effluent concentrations thus different average molecular weights from base assumptions; 3) circulating fluidized bed boilers are injected with limestone to control SO₂, limestone produces CO₂ not addressed by the F_(C) Factor; 4) many poor quality coals found in eastern Europe and from the Powder River Basin in the United States may have significant natural limestone in its fuel's mineral matter, thus producing effluent CO₂ not addressed by the F_(C) Factor; 5) the EPA requires the reporting of emission rates based on measured wet volumetric flow reduced to standard conditions, but the quantity of effluent moisture is not independently measured, whose specific volume varies greatly as a function of its molar fraction thus introducing a major source of error in using volumetric flow; and 6) ideal gas behavior is assumed adequate.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a block diagram illustrating the procedures involved in determining system heat rate using the F Factor.

DESCRIPTION OF THE PREFERRED EMBODIMENT The L Factor

This invention expands '711 by using its L′_(Fuel) quantity (or its equivalence the L_(Fuel) quantity), herein termed the L Factor, also known in '711 as the “fuel factor”, to compute a thermal system's heat rate. These teachings lead to the use of the F Factor to compute a thermal system's heat rate. L′_(Fuel) is defined by Eq.(72) of '711, repeated here with one change:

L′ _(Fuel)=10⁶ [x _(Dry-theor) N _(Dry-Fuel) +a _(Dry-theor)(1+φ_(Ref))N _(Dry-Air) −J _(theor) N _(H2O) −x _(MAF-theor)α_(MAF-10) N _(Ash)]/(x _(Dry-theor) N _(DryFuel) HHV _(Dry))  (72A)

The difference is the term φ_(Ref) (which is the ratio of non-oxygen gases to oxygen used for ambient air conditions in Eq.(72A) and elsewhere by this invention, and is further discussed in '711), which was changed from φ_(Act). This invention teaches that φ_(Ref) must be employed since changes in combustion air's oxygen content should not effect the computed L Factor. The preferred embodiment when computing the L Factor is to set φ_(Ref)=3.773725 as effects the determination of the L Factor; but also having an acceptable range such that φ_(Ref) is greater than a value of 3.7619 and less than a value of 3.7893 [i.e., 0.2088<A_(Ref)<0.2100, where φ_(Ref)=(1−A_(Ref))/A_(Ref)]. The equivalence of L′_(Fuel) is L_(Fuel), and is defined in words between Eqs.(75) and (76) in '711. When the quantities x, a and J of '711 are in per cent, the calculational base is therefore 100 moles of dry gas, thus:

L _(Fuel)=10⁶[100N _(DryGas/theor)]/(x _(Dry-theor) N _(Dry-Fuel) HHV _(Dry))  (75A)

As fully explained in '711, the numerators of the right sides of these two equations are developed from the same mass balance equation involving dry fuel and stoichiometrics associated with theoretical combustion (also called stoichiometric combustion):

[x _(Dry-theor) N _(Dry-Fuel) +a _(Dry-theor)(1+φ_(Ref))N _(Dry-Air) −J _(theor) N _(H2O) −x _(MAF-theor)α_(MAF-10) N _(Ash)]=[100N _(DryGas/theor)]  (80)

Eq.(80) states that dry fuel, plus theoretical combustion air, less effluent water, less effluent ash results in dry gaseous total effluents associated with theoretical combustion. Eq.(80) is the bases for the L Factor; i.e., when each side of Eq.(80) is divided by x_(Dry-theor)N_(Dry-Fuel)HHV_(Dry). This is fundamentally different than EPA's F Factor method. Although Eqs.(72A) & (75A) employ molar quantities, use of molecular weights results in a mass-base for the L Factor, and thus for Eq.(80). Unlike the F Factor, ideal gas assumptions are not applied nor needed. The molecular weight of the dry gas total effluents associated with theoretical combustion is the term N_(DryGas/theor) (the identical quantity is denoted as N_(Dry-Gas) in '711), its associated mass-base, or mass flow rate, is denoted as m_(DryGas/theor). Common engineering units for the L Factor, which are perferred, are pounds_(Dry-effluent)/million-Btu_(Fuel), or its equivalence; units of feet³ _(Dry-effluent)/million-Btu_(Fuel), or its equivalence, may also be employed. The L Factor expresses the “emission rate” for dry gaseous total effluents from theoretical combustion of dried fuel.

For a coal fuel, having a unique Rank or uniquely mined, the L Factor has been shown to have a remarkable consistency to which this invention makes unique advantage when applied in determining heat rate. Standard deviations in L_(Fuel), for coals range from 0.02% (for semi-anthracite), to 0.05% (for medium volatile bituminous), to 0.28% (for lignite B). Table 1 illustrates this, obtained from F. D. Lang, “Monitoring and Improving Coal-Fired Power Plants Using the Input/Loss Method—Part II”, ASME, 1999-IJPGC-Pwr-34, pp.373-382. Listed in the third and fourth columns are standard deviations, in engineering units. Table 1 also presents moisture-ash-free higher heating values and computed F_(C) Factors.

This paragraph discusses several definitions which are useful in understanding this invention. First, As-Fired fuel energy flow is numerically is the same as dry fuel energy flow for either actual combustion or theoretical combustion: m_(As-Fired)HHV=m_(DryFuel/Act)HHV_(Dry), or m_(As-Fired/theor) HHV=m_(DryFuel/theor)HHV_(Dry). Also the following equalities relating fuel energies, are important when correcting the L Factor to wet fuel conditions: x_(MAF-theor)N_(MAF-Fuel)HHV_(MAF)=x_(Dry-theor)N_(DryFuel) HHV_(Dry)=x_(Wet-theor)N_(Wet-Fuel)HHV. However, the dry fuel energy flow based on actual combustion is not the same as dry fuel energy flow based on theoretical combustion as required in Eqs.(72A) & (75A): m_(DryFuel/Act)HHV_(Dry)≠m_(DryFuel/theor)HHV_(Dry). Second, the US Environmental Protection Agency (EPA) requires the measurement of the actual total effluents flow from most fossil-fired systems, discussed in '711. Although reported for the EPA in volumetric flow at standard conditions, this invention teaches the conversion of measured total effluents flow to a mass-base using hot densities (not cold). This is not the same total effluents mass flow associated with theoretical combustion, on a dry-base termed m_(DryGas/theor), or the wet-base m_(WetGas/theor). This invention also teaches, under certain conditions, to replace the total effluents flow measurement with the system's indicated fuel flow when determining heat rate. Third, the conversion from any efficiency (η) to a heat rate (HR) is common art; for example, the system heat rate is defined as HR_(system)=3412.1416/η_(system) where the constant converts units from Btu/hr to kilowatts, thus HR in units of Btu/kW-hr, or its equivalence.

TABLE 1 L Factors and F_(C) Factors for Various Coal Ranks (L_(Fuel) and F_(C) in units of lbm/million-Btu, HHV in Btu/lbm) No. Com- of Heating Value puted Sam- HHV_(MAF) ± L Factor F_(C) Coal Rank ples ΔHHV_(MAF) L_(Fuel) ± ΔL_(Fuel) Factor Anthracite 29 14780.52 ± 262.65 827.55 ± 1.62 2035 (an) Semi-Anthracite 16 15193.19 ± 227.41 804.10 ± 0.19 1916 (sa) Low Vol. 89 15394.59 ± 435.54 792.82 ± 0.39 1838 Bituminous (lvb) Med. Vol. 84 15409.96 ± 491.21 786.60 ± 0.41 1593 Bituminous (mvb) High Vol. A Bit. 317 15022.19 ± 293.35 781.93 ± 0.98 1774 (hvAb) High Vol. B Bit 152 14356.54 ± 304.65 783.08 ± 1.58 1773 (hvBb) High Vol. C Bit 189 13779.54 ± 437.67 784.58 ± 1.55 1797 (hvCb) Sub-Bituminous 35 13121.83 ± 355.55 788.25 ± 1.07 1867 A (subA) Sub-Bituminous 56 12760.63 ± 628.26 787.07 ± 1.13 1862 B (subB) Sub-Bituminous 53 12463.84 ± 628.26 788.67 ± 3.07 1858 C (subC) Lignite A 76 12052.33 ± 414.79 796.52 ± 1.53 1905 (ligA) Lignite B 25 10085.02 ± 180.09 765.97 ± 2.11 1796 (ligB)

This invention teaches that first correcting L_(Fuel) from conditions associated with theoretical combustion to actual conditions, and then dividing the corrected L_(Fuel) into the measured total effluents mass flow rate, the total fuel energy flow, m_(As-Fired) (HHVP+HBC), is then derived (termed the “As-Fired” fuel energy flow).

 m _(As-Fired)(HHVP+HBC)=10⁶Ξ_(Gas) m _(DryGas/Act) /[L _(Fuel)Ξ_(AF)]  (81)

where the units of mass flow (m) are lbm/hr, corrected heating value (HHVP) and Firing Correction (HBC) in Btu/lbm, and the L Factor in lbm/million-Btu. Ξ_(Gas) and Ξ_(AF) are unitless correction factors and discussed below.

From Eq.(81) As-Fired fuel mass flow may then be determined if heating value and the Firing Correction have been determined:

m _(As-Fired)=10⁶Ξ_(Gas) m _(DryGas/Act) /[L _(Fuel)Ξ_(AF)(HHVP+HBC)]  (82)

As is common art for an electric power plant, dividing m_(As-Fired) (HHVP+HBC) by the total useful output, denoted as P in kilowatts, see '711 Eq.(1), system heat rate (also termed “gross unit heat rate” or “gross heat rate”) is then determined by invoking Eq.(81). A “net heat rate” may also be determined for any heat rate relationship taught herein by replacing P with P minus House Load; the House Load being the system's internal consumption of power.

HR _(system)=10⁶Ξ_(Gas) m _(DryGas/Act) /[L _(Fuel)Ξ_(AF) P]  (83)

'711 teaches the determination and use of HHVP and HBC. Alternatively, for situations where heating value may be reasonably estimated the methods of '711, developing HHVP from first principles, need not apply. Further, the HBC term could be assumed to have negligible effect and thus taken as zero, computed using '711 procedures, or estimated and/or held constant. HBC and HHVP are included here to illustrate consistency with '711 and '198. The L_(Fuel) parameter is typically based on an uncorrected heating value, HHV, thus requiring a HHV/(HHVP+HBC) correction within the Ξ_(AF) term, see Eqs.(84A), (84B) & (84C). The corrected heating value, HHVP, defined in '711, could be used to develop L_(Fuel), but is not preferred.

In Eqs.(81), (82) & (83), Ξ_(Gas) is a correction factor for measurement error in the total effluents flow. As a defined thermodynamic factor addressing conceptual corrections, Ξ_(AF) principally converts conditions associated with theoretical combustion to those associated with the actual (As-Fired) conditions, thus allowing the use of the L Factor to monitor actual conditions. The combined L_(Fuel)Ξ_(AF) expression is termed the corrected L Factor, that is, producing actual total effluents mass flow divided by the actual As-Fired fuel energy flow, and which is normalized to the bases of efficiency used at a given facility. For example, if the power plant uses HHV, then the term HHV/(HHVP+HBC) would not appear in Eqs.(84A), (84B) or (84C); if only HHVP is used then the term HHV/HHVP would appear. This is termed the correction for the system heating value base. Use of (HHVP+HBC) as a bases is preferred when correcting the L Factor.

Ξ_(AF) =[m _(DryGas/Act) m _(WetFuel/theor)/(m _(DryGas/theor) m _(As-Fired))]HHV/(HHVP+HBC)  (84A)

Ξ_(AF) =[q _(DryGas/Act)ρ_(DryGas/Act) m _(WetFuel/theor)/(q _(DryGas/theor)ρ_(DryGas/theor) m _(As-Fired))]HHV/(HHVP+HBC)  (84B)

Ξ_(AF/Gas)=(q _(DryGas/Act) m _(As-Fired))(m _(WetFuel/theor) /m _(DryGas/theor))HHV/(HHVP+HBC)  (84C)

Eqs.(84A) and (84B) are equivalent, however Eq.(84B) is presented to indicate a conversion of total effluents mass flow to volumetric flow, where q_(DryGas/Act) and q_(DryGas/theor) are dry-base volumetric flows associated with actual and theoretical combustion. Eq.(84B) illustrates the importance of considering compatible gaseous densities, ρ_(DryGas/Act) and ρ_(DryGas/theor), whereas if not applied consistently, or assumed the same thus cancelling, could possibly incorrectly bias Ξ_(AF). Eq.(84C) may be employed if the effluent flow is expressed in terms of volumetric flow; if used, Ξ_(AF/Gas) carries the units of ft³-Dry Gas/lbm-As-Fired fuel.

Although L_(Fuel) is based on dry fuel energy flow associated with theoretical combustion, the ratio m_(DryFuel/theor)/m_(DryFuel/Act) is equivalent to the ratio m_(WetFuel/theor)/m_(As-Fired), allowing Ξ_(AF) of Eq.(84A) or (84B) to correct the denominator of L_(Fuel) such that its bases is the As-Fired (actual, wet) fuel conditions.

When the total effluents flow is measured on a wet-base, m_(WetGas/Act), L_(Fuel) is further corrected with the term (1−WF_(H2O)), where WF_(H2O) is the weight fraction of moisture determined to be in the wet total effluents. The factor (1−WF_(H2O)) converts the L_(Fuel)'s numerator from a dry-base to a wet-base expression of the total effluents mass. The preferred embodiment is to use a dry-base total effluents which involves less uncertainty given possible inaccuracies in determining WF_(H2O). However, WF_(H2O) may be determined by measurement of the volume (molar) concentration of effluent moisture and converting to a mass-base, or through computer simulation of the system or otherwise estimated. As applied: Ξ_(AF/Wet)=Ξ_(AF)/(1−WF_(H2O)), the corrected L Factor then being the quantity L_(Fuel)Ξ_(AF/Wet). This correction is termed conversion to a wet-base L Factor.

'711 teaches that turbine cycle energy flow (termed BBTC, having typical units of Btu/hr) may be used to compute As-Fired fuel flow, via its Eq.(21). However, this may also be used toovercheck the above Eq.(82)'s fuel flow, or Eq.(81)'s fuel energy flow, given a determined boiler efficiency.

 m′ _(As-Fired) =BBTC Ξ _(TC)/[η_(Boiler)(HHVP+HBC)]  (85A)

m′ _(As-Fired)(HHVP+HBC)=BBTCΞ_(TC)/η_(Boiler)  (85B)

Boiler efficiency may be determined by: 1) estimation by the power plant engineer; 2) methods of '711; 3) held constant; 4) determined using the methods of the American Society of Mechanical Engineers (ASME), Performance Test Codes 4.1 or 4; 5) the methods described in the technical paper: F. D. Lang, “Monitoring and Improving Coal-Fired Power Plants Using the Input/Loss Method—Part III”, ASME, 2000-IJPGC-15079 (CD), July 2000; 6) the methods described in the technical paper: T. Buna, “Combustion Calculations for Multiple Fuels”, ASME Diamond Jubilee Annual Meeting, Chicago, Ill., Nov. 13-18, 1955, Paper 55-A-185; or 7) the methods described in the technical paper: E. Levy, et al., “Output/Loss: A New Method for Measuring Unit Heat Rate”, ASME, 87-JPGC-PWR-39, October 1987.

The term Ξ_(TC) is a factor chosen such that the computed fuel flow from Eq.(85A), m′_(As-Fired), and that of Eq.(82) have reasonable agreement. An alternative approach is to choose Ξ_(TC) of Eq.(85B) such that the computed fuel energy flow, m′_(As-Fired) (HHVP+HBC), and that of Eq.(81) have reasonable agreement. For the typical power plant situation, the greatest uncertainty in these relationships, or in Eq.(21) of '711, lies with the turbine cycle energy flow, BBTC; provided HHVP (or HHV) is known. Thus the factor Ξ_(TC) is used to adjust and correct the BBTC quantity until fuel flow, and/or fuel energy flow, from the two methods have reasonable agreement. Broadly, Ξ_(TC) is a general correction to the turbine cycle energy flow; however errors in boiler efficiency and/or heating value are also addressed. The advantage of this technique lies in its foundation with the demonstrated consistency ofthe L Factor. This invention teaches that such comparisons are possible since Eqs.(85A) & (82), and Eqs.(85B) & (81), are independently developed having completely different bases. With adjustments using Ξ_(TC), the turbine cycle heat rate may be determined:

HR _(turbine-cycle) =BBTC Ξ _(TC) /P  (86)

The L Factor method may be further extended to eliminate the requirement to measure total effluents flow, replaced with a fuel flow measurement. This may be accomplished by simplification of Ξ_(AF) to the following given cancellation of the m_(DryGas/Act) term; see Eqs.(83) & (84A), reduced to Eq.(87A). Also, anticipating the cancellation of volumetric flow measurement of effluent flow, and use of the F_(C) Factor, Eq.(84C) may be used to develop Eq.(87B):

Ξ_(FG)=(m _(WetFuel/theor) /m _(DryGas/theor))HHV/(HHVP+HBC)  (87A)

 Ξ_(FG/Fuel)=(m _(WetFuel/theor) /m _(As-Fired))]HHV/(HHVP+HBC)  (87B)

Thus, using Eq.(87A):

m _(As-Fired)(HHVP+HBC)=10⁶Ξ_(Fuel) m _(AF/On-L) /[L _(Fuel)Ξ_(FG)]  (88)

m _(As-Fired)=10⁶Ξ_(Fuel) m _(AF/On-L) /[L _(Fuel)Ξ_(FG)(HHVP+HBC)]  (89)

HR _(system)=10⁶Ξ_(Fuel) m _(AF/On-L) /[L _(Fuel)Ξ_(FG) P]  (90)

where the quantity Ξ_(FG) may be computed explicitly knowing only the fuel chemistry, the correction for the system heating value base, and assuming theoretical combustion. In Eqs.(88), (89) & (90), Ξ_(Fuel) is a correction factor for measurement error in the unit's indicated As-Fired fuel flow measurement, termed m_(AF/On-L). The advantage of using Ξ_(FG), and Eqs.(88), (89) & (90), lies when the fuel flow measurement, although typically not accurate in coal-fired plants, is a consistent measurement, thus correctable through Ξ_(Fuel). Further, the Ξ_(FG) quantity is constant for a given fuel, and easily calculated. Although Eq.(90) reduces to [m_(As-Fired/Act)(HHVP+HBC)/P], the classical definition of HR_(system) Eq.(90) is composed of quantities which could be measured on-line if having the necessary consistently (in the system's indication of fuel flow, m_(AF/On-L), and P). It also has usefulness to check the measured total effluents flow by equating Eqs.(81) and (88) and solving for m_(DryGas/Act). Eq.(90) has applicability for fuels with highly variable water and ash contents, but where L_(Fuel) is constant (as has been demonstrated in Table 1, e.g., lignite fuels). Eq.(89) may also be used for checking the indicated fuel flow, or fuel energy flow via Eq.(88), with the tested or observed quantity.

Additionally, this invention is not limited by the above presentations. Heating value could be computed using Eqs.(81) and (85A), or Eq.(88), provided fuel flow is independently determined. When using the L Factor, and when off-line, its computation via Eqs.(81), (82) & (83) represent the preferred embodiment.

Evaluating the Ξ_(AF) and Ξ_(FG) Corrections

As taught by this invention if heat rate of a fossil-fired system is to be evaluated using the methods of this invention, the correction terms Ξ_(AF), Ξ_(AF/Gas), Ξ_(FG) or Ξ_(FG/Fuel), must be determined. Several of these terms employ the ratio m_(WetFuel/theor)/m_(DryGas/theor). This ratio is equal to x_(Wet-theor)N_(Wet-Fuel)/(100N_(WetGas/theor)) computed using Eq.(80) assuming wet-base quantities. Eq.(80), based on theoretical combustion, may be evaluated knowing only the fuel's chemistry. The Ξ_(AF) term contains the ratio (m_(DryGas/Act)/m_(As-Fired)) which is equal to the quantity [(1.0+AF_(Wet/Act))/(1.0−WF_(H2O)−WF_(Ash))], where: AF_(Wet/Act) is the system's actual Air/Fuel ratio, WF_(H2O) is the wet-base effluent moisture weight fraction, and WF_(Ash) is the wet-base effluent ash weight fraction. The ratio m_(WetFuel/theor)/m_(As-Fired) is also used which may be evaluated as unity if the system employs low excess combustion oxygen, or computed as the ratio: (η_(Boiler)/η_(Boiler/theor)); where η_(Boiler) is the actual boiler efficiency and η_(Boiler/theor) the boiler efficiency assuming theoretical combustion. η_(Boiler) may be computed from any accurate method which is not dependent on any measured flow (i.e., fuel, air, total effluents nor working fluid); examples of such methods are discussed following Eq.(85B). η_(Boiler) may be computed using these same methods, but assuming theoretical combustion. These correction terms may also be determined by assumption, estimation or gathering from a data base associated with historical combustion air flow and/or fuel flow determinations.

The F Factor

The following discusses the EPA's F Factor in light of its use in determining the L Factor, fuel energy flow and/or system heat rate. For those situations in which the computations leading to the L Factor are inconvenient or troublesome, then use of the F Factor can afford reasonable accuracy, and then becomes the preferred embodiment. In this context, use of the F_(C) Factor to determine the emission rate for dry gaseous total effluents assuming theoretical combustion is given by Eq.(91A) or Eq.(91B), which are alternative methods for computing the L Factor, but with less accuracy. A validity test for use of the F_(C) Factor lies in whether Eq.(91A) produces the same values as obtained from Eqs.(72A) or (75A); and, furthermore, whether these values are at least as consistent as observed with actual fuel data, and especially for coal data as observed in Table 1. The L Factor as computed from the F_(C) Factor is herein termed L_(Fuel/EPA). L_(Fuel/EPA) is corrected with the Ξ_(AF) or Ξ_(FG) term as taught above, resulting in a corrected L Factor.

L _(Fuel/EPA)=100N _(DryGas/theor) F _(C)/(385.321d _(theor)); lbm-Dry Gas/million-Btu  (91A)

L _(Fuel/EPA)=100F _(C) /d _(theor); ft³-Dry Gas/million-Btu  (91B)

N_(DryGas/theor) is the molecular weight of the dry gaseous total effluents assuming theoretical combustion, and d_(theor) is the concentration of CO₂ at the system's boundary on a dry-base (in per cent) given theoretical combustion. d_(theor) may be computed based on known fuel chemistry; or it may be obtained by applying a correction factor to the actual concentration of CO₂, such correction based on periodic computations and measurements, or otherwise obtained. Reference should be made to '198 and '711 for encompassing stoichiometrics. It is instructive to examine the units of Eqs.(91A) and (91B); note that in the following “Dry Gas” refers to the total effluents assuming theoretical combustion, and, for clarity, assume a volume base replaces molar quantities. F_(C) carries units of ft³-CO₂/million-Btu. If L_(Fuel/EPA) is used conventionally, that is with units of lbm-Dry Gas/million-Btu, applicable units for Eq.(91A) are:

lbm-Dry Gas/million-Btu [=][(100 ft³-Dry Gas/base)(lbm-Dry Gas/lbm-mole Dry Gas)(ft³-CO₂/million-Btu)]/[(385.321 ft³-Dry Gas lbm-mole Dry Gas)·{(ft³-CO₂/ft³-Dry Gas)(100 ft³-Dry Gas/base)}]

Alternatively, if L_(Fuel/EPA) is used with units of ft³-Dry Gas/million-Btu, applicable units for Eq.(91B) are:

ft³-Dry Gas/million-Btu [=][(100 ft³-Dry Gas/base)(ft³-CO₂/million-Btu)]/{(ft³-CO₂/ft³-Dry Gas)(100 ft³-Dry Gas/base)}

These presentations reveal that inclusion of the gas molecular weight is necessitated for units consistency for Eq.(91A). Note that the 385.321 volume to molar conversion is applicable for either dry or wet gas if ideal gas laws may be applied, and as required by the choice of the molecular weight being either dry- or wet-base. These presentations also teach that F_(C) must be divided by the CO₂ concentration (the last term in {braces}) such that units of ft³-CO₂ cancel. The units of F_(C) and the constant 385.321 are associated with simple ideal gas conversions, without consideration nor dependency on the actual combustion process. The CO₂ concentration is associated with theoretical combustion, d_(theor). The results of (91A) or (91B) is lbm or ft³ of dry gas associated with theoretical combustion per million Btu of fuel; thus these presentations teach the need for a correction from the theoretical to the actual via the term Ξ_(AF). The EPA factor F_(D), employing dry-base effluent O₂, and the factor F_(W) employing wet-base effluent O₂, require similar treatment.

The F_(C), F_(D) or F_(W) factors may be determined: 1) by computation based on fuel chemistry using EPA procedures; 2) by using constant values as suggested by the EPA for certain fuels; or 3) by using F_(C) values from Table 1. Also, F_(C) may be computed directly from Eqs.(91A) or (91B) by solving for F_(C) based on a known L Factor (L_(Fuel/EPA)), the theoretical concentration of effluent CO₂, and/or molecular weight N_(DryGas/theor). The bases and general accuracy of the F Factors is discussed in the technical paper: F. D. Lang and M. A. Bushey, “The Role of Valid Emission Rate Methods in Enforcement ofthe Clean Air Act”, Proceedings of Heat Rate Improvement Conference, Baltimore, Md., sponsored by Electric Power Research Institute, May 1994 (also published in: FLOWERS '94: Proceedings of the Florence World Energy Research Symposium. editor E. Carnevale, Servizi Grafici Editoriali, Padova, Italy 1994). Lang and Bushey used the symbol β_(CO2-dry) for d_(Act) (as used here and in '711), and E for emission rate whereas ER is used here and in '711.

EPA regulations rely on F Factors to describe the dry pounds ofthe total effluents per million-Btu of fuel burned, for actual conditions found at any stationary source offossil combustion. This may be adequate for EPA's environmental protection policies; it is not accurate compared to this invention's use of L Factor methodology and L_(Fuel) based on Eqs.(72A) or (75A). This invention teaches by the very nature of the F Factor formulation used by the EPA, errors must be realized when these uncorrected factors are employed for actual combustion situations. As found in the course of developing this invention, the definition of the L Factor intrinsically involves effluent water and effluent ash, see Eq.(72A); F_(C), F_(D) or F_(W) factors do not, they are simple conversions of fuel to effluents using ideal gas assumptions, without consideration of basic combustion. The effects of differing water (both entrapped and that created from combustion) and ash contents associated with hydrocarbon fuels, being subtracted from fuel and combustion air terms of Eq.(72A), are conceptually important. These effects are addressed by this invention. Use of an F Factor derived without consideration of basic combustion, results in an inaccurate L Factor. For example, L_(Fuel) for average hvAb coal based on 317 samples is 781.93 lbm/million-Btu, while L_(Fuel/EPA) is 773.81 or 1.05% difference; the standard deviation for this large sample size is only 0.13% based on Eq.(72A). The error in L_(Fuel/EPA) amounts to over 100 ΔBtu/kW-hr in heat rate.

Table 2 presents typical sensitivities of L_(Fuel) and Ξ_(AF) for actual combustion situations. In Table 2 the R_(Act) term is the air pre-heater “leakage factor” discussed in '711; the A_(Act) term is also defined and used throughout '711, yielding φ_(Act)=3.82195 for the example; by “boiler” in the last two lines is meant the excess O₂ measurement is taken at the combustion gas inlet to the air pre-heater, before dilution by air pre-heater leakage. The last case studied varied the A_(Act) term, thus φ_(Act), which effects the mass of dry total effluents although not the fuel per se.

TABLE 2 Typical Sensitivities of L_(Fuel) and Ξ_(AF) for hvAb Coal L_(Fuel), Ξ_(AF) Correction, hvAb Case Eq. (75A) Eqs. (84A) Theoretical Combustion 781.93 1.00000 1.0% excess O₂, R_(Act) = 1.00. 781.93 1.04664 2.0% excess O₂, R_(Act) = 1.00. 781.93 1.09820 3.0% excess O₂, R_(Act) = 1.00. 781.93 1.15551 3.0% excess O₂ (boiler), and R_(Act) = 1.10 781.93 1.26410 3.0% excess O₂ (boiler), 781.93 1.27821 R_(Act) = 1.10, and A_(Act) = 0.207385.

If F Factors are to be used to produce the L Factor, this invention teaches that, for example, Eq.(91A) and (91B) must be used with caution, and that applying numerical bias or a determined correlation to the resulting heat rate must be considered.

The following equations apply for determining fuel flow and system heat rate based on the F_(C) Factor, employing mass or volumetric flows, the preferred embodiment when using the F_(C) Factor, as discussed above.

m _(As-Fired)=385.321×10⁶Ξ_(Gas) m _(DryGas/Act) d _(theor)/[100N _(DryGas/theor) F _(C)Ξ_(AF)(HHVP+HBC)]  (92A)

m _(As-Fired)=385.321×10⁶Ξ_(Gas) m _(WetGas/Act) d _(theor)/[100N _(DryGas/theor) F _(C)Ξ_(AF/Wet)(HHVP+HBC)]  (92B)

m _(As-Fired)=10⁶Ξ_(Gas) q _(DryGas/Act) d _(theor)/[100F _(C)Ξ_(AF/Gas)(HHVP+HBC)]  (92C)

m _(As-Fired)=10⁶Ξ_(Gas) m _(DryGas/theor) d _(theor)/[100F _(C)Ξ_(FG/Fuel)(HHVP+HBC)]  (92D)

HR _(system)=385.321×10⁶Ξ_(Gas) m _(DryGas/Act) d _(theor)/[100N _(DryGas/theor) F _(C)Ξ_(AF) P]  (92A)

HR _(system)=385.321×10⁶Ξ_(Gas) m _(WetGas/Act) d _(theor)/[100N _(DryGas/theor) F _(C)Ξ_(AF/Wet) P]  (92B)

HR _(system)=10⁶Ξ_(Gas) q _(DryGas/Act) d _(theor)/[100F _(C)Ξ_(AF/Gas) P]  (92C)

HR _(system)=10⁶Ξ_(Gas) m _(DryGas/theor) d _(theor)/[100F _(C)Ξ_(FG/Fuel) P]  (92D)

In these relationships, m_(DryGas/Act) or m_(WetGas/Act) are the dry-base or wet-base mass flow rates (lbm/hour) of total effluents, q_(DryGas/Act) or q_(WetGas/Act) are the volumetric flow rates (ft3/hour), d_(theor) is the CO₂ effluent concentration on a dry-base assuming theoretical combustion, N_(DryGas/theor) is the molecular weight of the dry-base total effluents assuming theoretical combustion, and WF_(H2O) is the actual wet-base weight fraction of effluent H₂O consistent with the determination of m_(WetGas/Act). m_(DryGas/Act) could be substituted with q_(DryGas/Act)ρ_(DryGas) if volumetric flow is measured; m_(WetGas/Act) could be substituted with q_(WetGas/Act)ρ_(WetGas). Use of (HHVP+HBC) in Eq.(92), versus simply HHV, or HHVP, is dependent on the chosen bases of system heating value base as discussed above. Multiplying both sides of Eq.(92) by (HHVP+HBC) produces total fuel energy flow as in Eq.(81). Eqs. of (93) states that heat rate is directly proportional to the total effluents flow and the CO₂ concentration associated with theoretical combustion, and inversely proportional to F_(C) and electrical power (kilowatts). These equations may be repeated using the F_(W) and F_(D) Factors, also described and allowed by 40 CFR Part 60, Appendix A, Method 19. Ξ_(Gas) may be taken as unity for Eq.(92D) & (93D) or otherwise determined.

The F_(D) and F_(W) Factors may be employed in similar relationships as taught herein. The above equations represent varieties of relationships involving the F_(C) Factor and corrections, others may be developed based on these teachings. For those situations calling for the use of the F_(C) Factor, then the preferred embodiment involves use Eqs.(92D) and (93D) since the computation of the Ξ_(FG/Fuel) is most direct and accurate, involving the ratio (η_(Boiler)/η_(Boiler/theor)), as taught above. Further, the quantity (m_(DryGas/theor)d_(theor)) used in Eqs.(92D) & (93D) may be determined from theoretical combustion knowing only the fuel chemistry.

On-Line Monitonn

The following presents a factor similar to Ξ_(AF), termed Ξ_(On-L), which is applied for on-line monitoring and may be determined from routine system operational data. Thus Ξ_(On-L) may be substituted for Ξ_(AF) to achieve on-line monitoring of heat rate. By on-line monitoring is meant the analysis of plant data using the methods of this invention in essentially real time, and/or simply the acquisition of plant data.

As taught, the L Factor requires corrections to the actual, from total effluents and fuel flows associated with theoretical combustion. The total effluents flow correction is developed by first dividing all terms of Eq.(80) by x_(Dry-theor)N_(Dry-Fuel), thus developing an Air/Fuel ratio (termed AF_(Dry-theor)), and then substituting L_(Fuel) from Eq.(75A):

1.0+AF _(Dry-theor)−(J _(theor) N _(H2O) +x _(MAF-theor)αMAF-10 N _(Ash))/(x _(Dry-theor) N _(Dry-Fuel))=10⁻⁶ L _(Fuel) HHV _(Dry)  (94)

The Air/Fuel ratio is the ratio of the mass flow of combustion air to the mass flow of the As-Fired fuel. The terms in Eq.(94) involving effluent moisture and ash may be expressed as fuel weight fractions given theoretical combustion. However, since only the influence of dry total effluents on L_(Fuel) is desired it has been found that only the As-Fired weight fraction of ash needs to be considered in practice:

1.0+AF _(Dry-theor) −WF _(Ash)≈10⁻⁶ L _(Fuel) HHV _(Dry)  (95)

or simplifying using a constant K₁ (=1.0−WF_(Ash)), descriptive of a given fuel:

K ₃ AF _(Wet-theor) +K ₁=10⁻⁶ L _(Fuel) HHV _(Dry)  (96)

where K₃ is a conversion from dry-base to wet-base for theoretical combustion. L_(Fuel)HHV_(Dry) is approximately constant for any operation burning the same fuel, even though the fuel's water content may vary considerably (as it does commonly with poorer quality coals). Thus the ratio of indicated system wet Air/Fuel ratio to the wet Air/Fuel ratio associated with theoretical combustion, addresses the correction for total effluents flow. The correction for fuel flow is addressed as the ratio of the system's indication of As-Fired fuel flow (m_(AF/On-L)) to the wet fuel flow associated with theoretical combustion (m_(WetFuel/theor)).

The following functionality has been found to yield good results while monitoring a system on-line, when the total effluents flow is being measured:

Ξ_(On-L) =[K ₂(AF _(Wet/On-L) +K ₁)m _(AF/On-L) ]HHV/(HHVP+HBC)  (97)

It has been found in practice that the system engineer may determine K₁ and K₂ quickly by adjustments to his/her on-line monitoring routines, on-line monitoring software, or to the plant's data acquisition computer, or by estimation. To determine reasonable initial estimates: K₁ may be computed as taught above, K₂=1.0/[(K₃AF_(Wet-theor)+K₁)m_(WetFuel/theo)] as based on theoretical combustion, and requiring adjustment for the type of flow being monitored either mass-base or volume-base (e.g., the conversion factor 385.321 ft³/lb-mole at standard conditions); and where K₃=1.0. Eq.(97) employs the system's on-line measurements of Air/Fuel ratio (AF_(Wet/On-L)) and the As-Fired fuel flow (m_(AF/On-L)). Eq.(97) could also be expressed in terms of the actual combustion air flow measurement, m_(Air/On-L):

 Ξ_(On-L) =[K ₂(m _(Air/On-L) +K ₁ m _(AF/On-L))]HHV/(HHVP+HBC)  (98)

Finally, the methods of this invention may be applied on-line using the following equations. In Eq.(99) q_(DryGas/Act) is the measured dry total effluents volumetric flow, typically reported by system instruments in units of ft³/hour. If the total effluents flow is reported as a mass flow then Eqs.(81), (82) and (83), would apply replacing Ξ_(AF) with Ξ_(On-L). The effluent density, termed ρ, must be consistent with the measurement base of the volumetric flow. The preferred embodiment when using Eqs.(99) or (100), is the use of hot flows with hot densities. The combined L_(Fuel)Ξ_(On-L) expression is termed the corrected L Factor.

HR _(system)=10⁶Ξ_(Gas) q _(DryGas/Act)ρ_(DryGas) /[L _(Fuel)Ξ_(On-L) P]  (99)

HR _(system)=10⁶Ξ_(Gas) q _(WetGas/Act)ρ_(WetGas)(1−WF _(H2O))/[L_(Fuel)Ξ_(On-L) P]  (100)

Thus the L Factor may be corrected to a dry-base or wet-base, reflecting the nature of the total effluents considered. To illustrate the accuracy of the L Factor method Table 3 presents results of using several of the procedures discussed. Its accuracy is considered exceptional.

TABLE 3 Typical Heat Rate Results for High Volatile A Bituminous (hvAb) Coal (using Ξ_(AF) from Table 2, Ξ_(On-L) via Eq. (97), Ξ_(Gas) = 1.000) Measured L Factor L Factor System Heat Rate, Heat Rate, Heat Rate Off-Line On-Line hvAb Case (Btu/kW-hr) Eq. (83) Eq. (99) Theoretical Combustion 8436 8436 8436 1.0% excess O₂, R_(Act) = 1.00. 8452 8452 8455 2.0% excess O₂, R_(Act) = 1.00. 8471 8469 8474 3.0% excess O₂, R_(Act) = 1.00. 8491 8488 8483 3.0% excess O₂ (boiler), 8530 8526 8526 and R_(Act) = 1.10 3.0% excess O₂ (boiler), 8535 8530 8529 R_(Act) = 1.10, and A_(Act) = 0.207385.

To apply the F_(C) Factor to the on-line monitoring of a power plant the following equations apply for either dry- or wet-base quantities:

HR _(system)=385.321×10⁶Ξ_(Gas) q _(DryGas/Act)ρ_(DryGas) d _(theor)/[100N _(DryGas/theor) F _(C)Ξ_(On-L/F) P]  (101)

HR _(system)=10⁶ q _(DryGas/theor) d _(theor)/[100F _(C)Ξ_(On-L/Fuel) P]  (102)

It has been found that the factor Ξ_(On-L/F), substituted for the factor Ξ_(On-L), discussed above, may be resolved via Eq.(103A1) or (103A2). The factor Ξ_(On-L/Fuel), substituted for the factor Ξ_(FG/Fuel), discussed above, may be resolved via Eq.(103B).

Ξ_(On-L/F) =[K _(2F)(AF _(Wet/On-L) +K _(1F))m _(AF/On-L) ]HHV/(HHVP+HBC)  (103A1)

Ξ_(On-L/F) =[K ₂(m _(Air/On-L) +K ₁ m _(AF/On-L))]HHV/(HHVP+HBC)  (103A2)

Ξ_(On-L/Fuel)=(η_(Boiler)/η_(Boiler/theor))HHV/(HHVP+HBC)  (103B)

where the factors K_(2F) and K_(1F) are adjusted such that the system operator's observations and those produced from Eq.(101) or (102) have reasonable agreement. The factor K_(1F) may be computed as taught for K₁, or otherwise determined; it generally may be held constant. The factor K_(2F) is typically estimated or otherwise determined, and may include functionalities related to moisture in the total effluents, As-Fired fuel moisture, addresses different flow measurements (volumetric- or mass-base), and/or a correlation which adjusts the Air/Fuel ratio using operational parameters. In practice, for a given thermal system, the factor K_(2F) is developed as a variable, having at least functionality with a measured moisture in the total effluents.

Emission Rates of Pollutants

The ability to compute As-Fired fuel flow based on the L Factor, as taught by this invention, allows the determination of pollutant emission rates (ER) typically required for regulatory reporting. As taught in '711, and its Eq.(70B) and associated discussion, the emission rate of any effluent species may be determined by knowing its molar fraction (i.e., its concentration) within the total effluents, molecular weight of the species and the moles of fuel per mole of effluent. The procedure for calculating emission rates may be greatly simplified using the L Factor, which also results in increased accuracy.

This invention includes the following relationship to calculate the emission rate of any species:

ER _(i) =L _(Fuel)Ξ_(AF)Φ_(Dry-i) N _(i)/[100N _(DryGas/Act)]  (104)

where Φ_(Dry-i) is the dry-base molar concentration of species i (in per cent), N_(i) is the species' molecular weight, and N_(DryGas/Act) (or N_(WetGas/Act)) is the molecular weight of the dry (or wet) total effluents for actual combustion. When on-line, the molecular weight ofthe total effluents, N_(WetGas/Act) or N_(DryGas/Act), may be held constant or computed knowing the fuel's chemistry and operating parameters as is discussed in '711 and '198. Asan example, for SO₂ effluent using the nomenclature of '711, see Eq.(29) of '711: Φ_(Dry-SO2)=k.

For any effluent measured on a wet-base (Φ_(Wet-i)):

ER _(i) =L _(Fuel)Ξ_(AF/Wet)Φ_(Wet-i) N _(i)/(100N _(WetGas/Act))  (105)

If using the L Factor to determine emission rates, then the preferred embodiment is to use Eq.(104) which involves less uncertainty given possible inaccuracies in determining WF_(H2O), discussed above. The factor Ξ_(AF) is defined by Eq.(84A). The factor Ξ_(On-L) may be substituted for Ξ_(AF) in Eqs.(104) and (105) as taught in Eqs.(97) and (98).

The accuracy of using the L Factor for computing emission rates is demonstrated by the L Factor's ability to match measured system heat rates (see above table). The L Factor may track operational changes, whereas the F Factor requires numerical bias or contrived correlations. As reported by Lang & Bushey, errors in emission rates based on the F Factor may exceed 10% for certain fuels, with common errors of 3%. The preferred embodiment of this invention when determining emission rates is to use the L Factor as taught by Eqs. (104) & (105), replacing EPA methods.

However, to improve how the US EPA determines emission rates the following relationship is herein taught. Improvements to EPA methods include the recognition that F_(C) is based on theoretical combustion, not actual, and that the terms N_(DryGas/theor), Ξ_(AF), and d_(theor) used in Eq.(106) corrects for this assumption. When required by environmental regulations to use the F_(C) Factor, then Eq.(106), demonstrating corrections to the F_(C) Factor, is the preferred embodiment.

ER _(i) =N _(DryGas/theor) F _(C)Ξ_(AF)Φ_(Dry-i) N _(i)/(385.321d _(theor) N _(DryGas/Act))  (106)

As explained above: N_(DryGas/theor) is the composite molecular weight of the dry-gas effluent based on theoretical combustion products; Ξ_(AF) is defined by Eqs.(84A) or (84B) or may be replaced with the term Ξ_(On-L) discussed through Eqs.(97) or (98), or the term Ξ_(On-L/F) discussed through Eqs.(103A1) or (103A2), and/or variations discussed; Φ_(Dry-i) is the concentration ofpollutant i; N_(i) is the molecular weight of the pollutant i; d_(theor) is the theoretical concentration of effluent CO₂; and N_(DryGas/Act) is the composite molecular weight of the actual dry-gas effluent. Further use of various forms of the L Factor and the F Factors as taught herein involving dry-base, wet-base, volumetric or mass flow rates can be applied to the determination of emission rates. Although the present invention has been described in considerable detail and variations with regard to certain preferred embodiments thereof (when using the L Factor or when using the F Factor), other embodiments within the scope of the present invention are possible without departing from the spirit and general industrial applicability of the invention. Accordingly, the general theme and scope of the appended claims should not be limited to the descriptions of the preferred embodiment disclosed herein.

The Drawing

FIG. 1 illustrates an important portion of this invention, the determination of system heat rate associated with afossil fueled power plant. Box 303 depicts the calculation ofthe L Factor defined by Eqs.(72A) or (75A), or otherwise determined as discussed herein, including the use of Eq.(91A) or (91B) if applicable, including the use of Table 1. When Table 1 L Factors are used, this invention teaches to use these factors within a 1% range of their mean value as presented in Table 1 for any given Rank of coal; said Rank being defined by ASTM standards such as D388, or similar standards; said Rank requiring knowledge ofthe coal's chemistry and other properties. Thus if such L Factors are to be employed, establishing the L Factor for the anthracite coal between 819.36 and 835.83 lbm/million-Btu, or establishing the L Factor for the semi-anthracite coal between 796.14 and 812.14 lbm/million-Btu, or establishing the L Factor for the low volatile bituminous coal between 784.97 and 800.75 lbm/million-Btu, or establishing the L Factor for the medium volatile bituminous coal between 778.81 and 794.47 lbm/million-Btu, or establishing the L Factor for the high volatile A bituminous coal between 774.19 and 789.75 lbm/million-Btu, or establishing the L Factor for the high volatile B bituminous coal between 775.33 and 790.91 lbm/million-Btu, orestablishingthe L Factor forthe high volatile C bituminous coal between 776.82 and 792.43 lbm/million-Btu, or establishing the L Factor for the sub-bituminous A coal between 780.45 and 796.14 lbm/million-Btu, or establishing the L Factor for the sub-bituminous B coal between 779.28 and 794.94 lbm/million-Btu, or establishing the L Factor for the sub-bituminous C coal between 780.86 and 796.56 lbm/million-Btu, or establishing the L Factor for the lignite A coal between 788.63 and 804.49 lbm/million-Btu, or establishing the L Factor for the lignite B coal between 758.39 and 773.63 lbm/million-Btu.

Box 301 depicts the measurement of electrical generation produced by the thermal system. Box 305 depicts the calculation of a correction to the L Factor, the term Ξ_(AF), Ξ_(AF/Wet), Ξ_(AF/Gas), Ξ_(FG) or Ξ_(FG/Fuel) defined by Eqs.(84A), (84B), (84C), (87A) or (87B), or otherwise determined as discussed herein, including dry-base to wet-base conversions. Box 307 depicts the multiplication of the L Factor by the correction to the L Factor. Box 309 depicts the determination of the total effluents flow from fossil combustion. Box 311 depicts the determination of a correction factor to the determined total effluents flow, termed Ξ_(Gas), and its consistent use with either a mass or volume, dry-base or wet-base, total effluents flow measurement. Box 313 depicts the multiplication of the total effluents flow by its correction factor. Box 315 depicts the calculation ofthe system's total fuel energy flow as taught, for example, through Eqs.(81), (88), and/or the discussion pertaining to Eqs.(92). Box 317 depicts the calculation of the heat rate of the system as taught, for example, thought Eqs.(83), (90), (93), (99) and/or (100).

For FIG. 1 and elsewhere herein, if used, the words “obtain”, “obtained”, “obtaining”, “determine”, “determined”, “determining” or “determination” are defined as measuring, calculating, assuming, estimating or gathering from a data base. The words “establish”, “established” or “establishing” are defined as measuring, calculating, assuming, estimating or gathering from a data base. The word “total effluents” is used to mean all products resultant from the combustion of fossil fuel as found at the point where the flow rate of these combustion products is obtained, for example all effluents exiting from the smoke stack, the smoke stack being the point of flow measurement. The word “effluent” refers to a single, unique, combustion product at the point where the flow rate of all combustion products is obtained, for example CO₂ found in the smoke stack. Further, the words “theoretical combustion” refers to the following conditions: 1) combustion of fossil fuel with just enough oxygen that none is found in the products of combustion; and 2) complete and ideal oxidation occurs such that no pollutants are found in the products of combustion (e.g., CO, NO, SO₃, unburned fuel, etc. are not present). The words “theoretical combustion” and “stoichiometric combustion” mean the same. The words “adjust” or “adjusting” means to correct to a determined value. The words “reasonable agreement” mean that two parameters which are being compared, agree in their numerical values within a determined range or per cent. 

What is claimed is:
 1. A method for quantifying the operation of a fossil-fired system, the method comprising the steps of: obtaining a concentration ofthe effluent CO₂ found in theoretical combustion products from the fossil-fired system; obtaining a total effluents flow rate from the fossil-fired system; obtaining a correction factor for the total effluents flow rate, resulting in a corrected total effluents flow rate; obtaining an F_(C) Factor; obtaining a correction factor to the F_(C) Factor which converts its applicability from theoretical combustion to combustion associated with the fossil-fired system, and, if applicable, the correction for the system heating value base, resulting in a corrected F_(C) Factor; and dividing the product of the corrected total effluents flow rate and the concentration of effluent CO₂ by the corrected F_(C) Factor, resulting in a total fuel energy flow of the system.
 2. The method of claim 1, wherein the steps of obtaining the total effluents flow rate and obtaining the correction factor for the total effluents flow rate, includes the steps of: obtaining a total effluents mass flow rate from the fossil-fired system; and obtaining a correction factor for the total effluents mass flow rate, resulting in the corrected total effluents flow rate.
 3. The method of claim 1, wherein the steps of obtaining the total effluents flow rate and obtaining the correction factor for the total effluents flow rate, includes the steps of: obtaining a total effluents mass flow rate from the fossil-fired system; obtaining a correction factor for the total effluents mass flow rate; obtaining a conversion from moles to volume; obtaining an average molecular weight of the total effluents; and obtaining the corrected total effluents flow rate by combining the total effluents mass flow rate, the correction factor for the total effluents mass flow rate, the conversion from moles to volume, and the average molecular weight of the total effluents.
 4. The method of claim 1, including additional steps, after the step of dividing, of: obtaining a produced electrical power from the fossil-fired system; and dividing the total fuel energy flow of the system by the produced electrical power, resulting in a heat rate of the fossil-fired system.
 5. The method of claim 1, including additional steps, after the step of dividing, of: obtaining a fuel heating value of the fuel consumed by the fossil-fired system; and dividing the total fuel energy flow of the system by the fuel heating value, resulting in a fuel flow rate of the fossil-fired system.
 6. The method of claim 5, including additional steps, after the step of dividing, of: obtaining a turbine cycle energy flow; obtaining a boiler efficiency; obtaining a turbine cycle based fuel flow rate by dividing the turbine cycle energy flow by the product of the boiler efficiency and the fuel heating value; and adjusting the turbine cycle energy flow until the turbine cycle based fuel flow rate and the fuel flow rate are in reasonable agreement.
 7. The method of claim 1, including additional steps, after the step of dividing, of: obtaining a fuel flow rate of the fossil-fired system; and dividing the total fuel energy flow of the system by the fuel flow rate, resulting in the fuel heating value of the fuel consumed by the fossil-fired system.
 8. The method of claim 7, including additional steps, after the step of dividing, of: obtaining a turbine cycle energy flow; obtaining a boiler efficiency; obtaining a turbine cycle based fuel heating value by dividing the turbine cycle energy flow by the product of the boiler efficiency and the fuel flow rate; and adjusting the turbine cycle energy flow until the turbine cycle based fuel heating value and the fuel heating value are in reasonable agreement.
 9. The method of claim 1, wherein the step of obtaining the correction to the F_(C) Factor includes the steps of obtaining a combustion air flow rate of the fossil-fired system by on-line monitoring; obtaining a fuel flow rate of the fossil-fired system by on-line monitoring; determining a correction for the system heating value base used by the fossil-fired system; obtaining a set of correction factors applied to the combustion air flow rate and to the fuel flow rate which allow agreement between the system operator's observations of heat rate and the predicted; combining the combustion air flow rate, the fuel flow rate, the correction for the system heating value if applicable, and the set of correction factors resulting in the correction to the F_(C) Factor.
 10. A method for quantifying the operation of a fossil-fired system through understanding the emission rate of a pollutant, the method comprising the steps of: obtaining an F_(C) Factor; obtaining a correction factor to the F_(C) Factor which converts its applicability from theoretical combustion to combustion associated with the fossil-fired system, and, if applicable, the correction for the system heating value base, resulting in a corrected F_(C) Factor; measuring a concentration of a pollutant effluent; obtaining a concentration ofthe effluent CO₂ found in theoretical combustion products from the fossil-fired system; obtaining a conversion from moles to volume; obtaining a set of molecular weights which include the average molecular weight of the total effluents based on actual combustion, the molecular weight ofthe total effluents based on theoretical combustion, and the molecular weight of the effluent; and combining the corrected F_(C) Factor, the concentration of a pollutant effluent, the concentration of the effluent CO₂, the conversion from moles to volume, and the set of molecular weights resulting in the emission rate of a pollutant.
 11. The method of claim 10, wherein the step of obtaining the concentration of the effluent CO₂ found in theoretical combustion products from the fossil-fired system includes the steps of: obtaining a concentration of the effluent CO₂ found in actual combustion products from the fossil-fired system; obtaining a correction factor which converts the concentration of the effluent CO₂ found in actual combustion products to the concentration ofthe effluent CO₂ found in theoretical combustion products, resulting in the concentration of the effluent CO₂ found in theoretical combustion products.
 12. The method of claim 1, wherein the step of obtaining the concentration of the effluent CO₂ found in theoretical combustion products from the fossil-fired system includes the steps of: obtaining a concentration of the effluent CO₂ found in actual combustion products from the fossil-fired system; obtaining a correction factor which converts the concentration of the effluent CO₂ found in actual combustion products to the concentration ofthe effluent CO₂ found in theoretical combustion products, resulting in the concentration of the effluent CO₂ found in theoretical combustion products. 